Acoustical Radiation and Scattering above an Impedance Plane

Abstract

Half–space acoustical problems are of great importance, since sound fields caused by radiation or scattering from complex structures are seldom found in the boundless infinite three–dimensional space. In many cases, a flat ground with a certain surface impedance confines the acoustical space as it encounters for example when treating problems of outdoor sound propagation. Whereas the boundary element method (BEM) is a mighty tool for predicting sound fields in unlimited space, the occurrence of an infinite plane and the associated additional discretization effort weakens the advantages of the classical BEM. One possible remedy is to use a Green’s function as a building block for the BEM which automatically satisfies the boundary condition at the infinite plane and to incorporate it into the BEM. In the present article, such a half–space Green’s function will be constructed, inserted into a direct BEM formulation, and positively tested by solving numerically several different problems of acoustical sound propagation over impedance planes.